Q.If the Marginal Propensity to Consume (MPC) in an economy is 0.8, calculate the investment multiplier. If autonomous investment increases by Rs. 200 crore, find the resulting total increase in national income.
Concept understanding — The Investment Multiplier
The investment multiplier (k) measures how a change in autonomous investment produces a larger, magnified change in equilibrium national income. It is defined as k=1−MPC1=MPS1.
The multiplier works because one person's spending is another person's income. An initial injection of investment is spent, re-spent, and spent again in successive rounds, so total income rises by a multiple of the original investment. The size of that multiple depends entirely on the MPC.
The formula
k=ΔIΔY=1−MPC1=MPS1
Since MPC + MPS = 1, (1−MPC)=MPS, so the multiplier is simply the reciprocal of the marginal propensity to save.
How and why it works
Suppose the government/firms invest an extra ₹100 and MPC = 0.8. The ₹100 becomes income for the recipients, who spend 80% (₹80); that ₹80 becomes income for others, who spend ₹64; and so on. The rounds form a geometric series: 100(1+0.8+0.82+…)=100×1−0.81=100×5=₹500.
Worked illustration
With MPC = 0.8: k=1/(1−0.8)=1/0.2=5. A ₹100 crore rise in investment raises national income by 5×100=₹500 crore. If MPC were 0.5, k=2, and the same investment would raise income by only ₹200 crore.
Key relationships
- Higher MPC → higher multiplier (more of each round is re-spent).
- Higher MPS → lower multiplier (more leaks out into saving each round).
- Minimum value of k is 1 (when MPC = 0); it rises towards infinity as MPC approaches 1.
Limitations (leakages)
The simple multiplier assumes a closed economy with no taxes and idle resources. In reality, leakages — saving, taxes, and imports — reduce the effective multiplier, and full-employment or supply bottlenecks blunt it.
Exam trap
The multiplier depends on MPC, not APC. Also remember it is a double-edged tool: just as a rise in investment multiplies income upward, a fall in investment multiplies income downward (the reverse multiplier). Its minimum value is 1, never zero.
Compute the multiplier k=1/(1-MPC), then multiply by the given change in investment to find the change in income.
Multiplier k=5; ΔY=k×ΔI=5×200=Rs.1,000 crore.
k=1/(1−0.8)=1/0.2=5. ΔY=k×ΔI=5×200=1000.
Investment multiplier k = 5; resulting increase in national income ΔY = Rs. 1,000 crore.
The investment multiplier is:
k=1−MPC1=1−0.81=0.21=5
Verification using MPS: since MPS=1−MPC=1−0.8=0.2, the equivalent formula k=1/MPS=1/0.2=5 gives the identical result, confirming the multiplier value.
The resulting change in income for the given ΔI=Rs.200 crore:
ΔY=k×ΔI=5×200=Rs.1,000 crore
This means the initial Rs. 200 crore investment injection, once all the successive rounds of re-spending by an economy with MPC=0.8 work themselves through, ultimately raises TOTAL national income by five times as much — Rs. 1,000 crore.
Multiplier k = 5 (verified identically via both 1/(1-MPC) and 1/MPS); the Rs. 200 crore rise in autonomous investment leads to a total increase in national income of Rs. 1,000 crore.
A common error is computing the multiplier as 1/MPC instead of 1/(1−MPC) — using 1/0.8=1.25 instead of the correct 1/0.2=5 badly understates the true multiplier effect; the denominator must always be the LEAKAGE (1 - MPC, i.e. MPS), never MPC itself.
- CA Foundation 2026Set may-20261 markMCQQ.There is an increase in the national income by ₹ 2,000 crores when there is an increase in investments by ₹ 1,600 crores. Calculate the marginal propensity to consume. (A) 0.80 (B) 0.50 (C) 0.20 (D) 0.40
›Reveal solutionSolution
Multiplier k = ΔY/ΔI = 1.25 ⇒ MPC = 1 − 1/k = 0.20.
Step 1 — Find the multiplier
k=ΔIΔY=16002000=1.25
Step 2 — Relate the multiplier to MPC
k=1−MPC1
Step 3 — Solve for MPC
1.25=1−MPC1
1−MPC=1.251=0.8
MPC=1−0.8=0.20
Step 4 — Eliminate the others
0.80 (A) is actually the MPS complement / value of 1−MPC, a tempting trap. 0.50 (B) and 0.40 (D) do not satisfy k=1.25.
Watch outDo not confuse the answer with 1−MPC=0.8; that is the MPS, not the MPC. The question asks for MPC.
TipQuick route: MPC = 1 − (ΔI/ΔY) = 1 − 1600/2000 = 1 − 0.8 = 0.20.
✓Final answer(C) 0.20
- CA Foundation 2026Set may-20261 markMCQQ.Which of the following statements correctly explains the relationship between Marginal Propensity to Consume (MPC), Marginal Propensity to Save (MPS), and the value of the investment multiplier? (A) Higher the MPC more will be the value of investment multiplier (B) Higher the MPS more will be the value of investment multiplier (C) Lower the MPC more will be the value of investment multiplier (D) Lower the MPS less will be the value of investment multiplier
›Reveal solutionSolution
Multiplier k = 1/(1 − MPC) = 1/MPS, so a higher MPC (lower MPS) gives a larger multiplier — statement (A).
Step 1 — State the multiplier formula
k=1−MPC1=MPS1
with the identity MPC + MPS = 1.
Step 2 — See how k responds to MPC and MPS
- A higher MPC makes the denominator (1 − MPC) smaller, so k is larger.
- Equivalently, a higher MPS makes k = 1/MPS smaller.
Step 3 — Test each statement
- (A) Higher MPC → higher multiplier — TRUE, matches the formula.
- (B) Higher MPS → higher multiplier — false (higher MPS lowers k).
- (C) Lower MPC → higher multiplier — false (lower MPC lowers k).
- (D) Lower MPS → lower multiplier — false (lower MPS raises k).
Step 4 — Numerical check
If MPC = 0.8, k = 1/0.2 = 5; if MPC rises to 0.9, k = 1/0.1 = 10. Higher MPC clearly gives a bigger multiplier, confirming (A).
Watch outMPC and MPS move in opposite directions (they sum to 1). Statements (B) and (D) get the direction of the MPS effect backwards.
TipRemember: more spending, less saving out of extra income (high MPC / low MPS) → a stronger multiplier.
✓Final answer(A) Higher the MPC more will be the value of investment multiplier
- CA Foundation 2025Set jan-20251 markMCQQ.In an economy investment expenditure is increased by ₹ 300 crores and marginal propensity to consume is 0.6. Calculate the total increase in income. (A) ₹ 300 crores (B) ₹ 100 crores (C) ₹ 650 crores (D) ₹ 750 crores
›Reveal solutionSolution
k=1−MPC1=2.5, so ΔY=k×ΔI=2.5×300=750 crores.
Step 1 — The multiplier formula
The investment multiplier links a change in investment to the eventual change in income:
k=1−MPC1=MPS1
Step 2 — Compute the multiplier
k=1−0.61=0.41=2.5
Step 3 — Apply it to the investment change
ΔY=k×ΔI=2.5×300=750 crores
Why the other options are wrong
- (A) ₹300 crores ignores the multiplier (assumes k = 1).
- (B) ₹100 crores has no valid derivation.
- (C) ₹650 crores mis-applies the multiplier arithmetic.
Watch outThe multiplier uses 1−MPC (which equals MPS) in the denominator, not MPC. Using 1/0.6 would wrongly give ≈1.67.
TipTwo quick steps: k=1/(1−MPC), then multiply by the change in investment — never by total investment.
✓Final answer(D) ₹ 750 crores
- CA Foundation 2025Set jan-20251 markMCQQ.The investment multiplier is defined as the ratio of : (A) change in investment due to change in saving (B) change in demand due to change in investment (C) change in consumption due to change in investment (D) change in national income due to change in investment
›Reveal solutionSolution
The investment multiplier is k=ΔIΔY — the ratio of the change in income to the change in investment.
Step 1 — Definition
When investment rises, the extra spending becomes someone's income, part of which is re-spent, and so on. The multiplier captures the total, magnified effect on national income:
k=ΔIΔY=1−MPC1
Step 2 — Read the ratio correctly
Income (ΔY) is on top, investment (ΔI) at the bottom. So the multiplier is 'change in national income due to change in investment'.
Step 3 — Why the other options are wrong
- (A) links investment to saving — that is not the multiplier.
- (B) 'change in demand due to change in investment' is loosely worded and not the standard definition.
- (C) links consumption to investment — again not the multiplier ratio.
Watch outKeep the ratio the right way up: ΔY/ΔI, income over investment. Inverting it gives 1/k=MPS, a different quantity.
TipTie the definition to the formula k=1/(1−MPC); its numerator is always the change in income.
✓Final answer(D) change in national income due to change in investment
- CA Foundation 2025Set sep-20251 markMCQQ.The maximum value of investment multiplier will be the infinity when the value of : (A) MPC is 1. (B) MPC is –1. (C) APC is 1. (D) MPS is –1.
›Reveal solutionSolution
k=1/(1−MPC) is infinite when 1−MPC=0, i.e. MPC = 1.
Step 1 — The multiplier formula
k=1−MPC1=MPS1
The multiplier grows as MPC rises toward 1 (equivalently, as MPS falls toward 0).
Step 2 — When does it become infinite?
A fraction blows up to infinity only when its denominator approaches zero:
1−MPC=0⇒MPC=1⇒MPS=0
With MPC = 1 every additional rupee of income is re-spent, so successive rounds of spending never leak away and the multiplier is theoretically infinite.
Why the other options are wrong
- (B) MPC = −1 and (D) MPS = −1 are economically impossible; MPC and MPS lie between 0 and 1.
- (C) APC = 1 concerns the AVERAGE (not marginal) propensity and does not set the multiplier's denominator to zero.
Watch outThe multiplier depends on the MARGINAL propensity (MPC/MPS), not the average (APC/APS). Choosing the APC option is the classic trap here.
TipRemember the two extremes: MPC = 0 ⇒ k = 1 (minimum); MPC = 1 ⇒ k = ∞ (maximum).
✓Final answer(A) MPC is 1.
- CA Foundation 2025Set sep-20251 markMCQQ.If national income increases from ₹ 500 crores to ₹ 2,500 crores due to an increase in investment of ₹ 200 crores, what will be the value of the Marginal Propensity to Consume (MPC) ? (A) 0.90 (B) 0.85 (C) 0.75 (D) 0.95
›Reveal solutionSolution
k=ΔY/ΔI=2000/200=10=1/(1−MPC) ⇒ MPC = 0.90.
Step 1 — Find the multiplier
k=ΔIΔY=2002,500−500=2002,000=10
Step 2 — Link the multiplier to MPC
k=1−MPC1⇒10=1−MPC1
Step 3 — Solve for MPC
1−MPC=101=0.1⇒MPC=0.90
Why the other options are wrong
MPC values of 0.85, 0.75 or 0.95 correspond to multipliers of about 6.7, 4 and 20 respectively — none of which equals the actual multiplier of 10 implied by the data.
Watch outCompute the CHANGE in income (ΔY = 2,000), not the final income (2,500). Using 2,500/200 gives a wrong multiplier of 12.5 and a wrong MPC.
TipTwo quick steps: multiplier = ΔY/ΔI, then MPC = 1 − 1/k. Here MPC = 1 − 1/10 = 0.90.
✓Final answer(A) 0.90
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